Exam 12: Dealing With Uncertainty and Risk

A company has developed a new product. Market price of the product is $10 per unit, variable costs are $6 per unit and total fixed costs are $100 000. Suppose that the company sets a target of $2 of profit per unit. How many units should be produced to meet the target?

Future annual revenue generated by a project is a random variable. Its probability distribution function is given as follows: What is the probability of annual revenue being higher than $30 000/year?

The first cost of a highway project is $1.5 million. Operating and maintenance costs were estimated at $50 000 per year. There will be zero salvage value of the highway after 20 years. As a result of this project, a recreational facility worth $10 000 per year in benefits will be destroyed. Assuming a 4% social discount rate, what is the break-even value of time savings to the highway users? How would this value change if social discount rate increased to 10%?

New software has been developed, and $23 000 has been spent on its development. However, the implementation phase requires an additional $30 000. There is uncertainty about annual net revenue. Three potential scenarios with their probabilities of occurring were identified., as shown in the following table: Assume a 10% MARR and use a decision tree to answer the following question: What is the expected PW for deciding whether or not to proceed?

You have a contract with a company in the remote country of Placidia which guarantees you a profit of 100 000 Placidos in five years time. At the moment, one Placido is equal to one Canadian dollar. However, there is about to be an election in Placidia, and if the Placidia First candidate gets in, it is expected that there will be 10% annual inflation in Placidia over the next five years. As far as you can tell, each of the two candidates has an equal chance of being elected. If your MARR is 10%, what is the expected present value to you of the contract, in Canadian dollars?

You are experimenting with a process for producing high-energy-density batteries. You have a contract with the government to deliver a batch of 20 batteries, due today. If you deliver them on time and they are all functional, you will get $100 000. Each battery has a 1% chance of being defective, and if any of them are defective, the government will not pay you the $100 000, but will fine you $10 000. What is the expected value to you of your contract with the government?

An engineering project involves reinforcing a concrete beam. From previous experience it is thought that the probability of corrosion is 1%. A diagnostic test is performed on the reinforced beam. If corrosion is present, then the probability that the test will reveal it is 80% while the probability that the test will miss it is 20%. The diagnostic never yields false positives-that is, it will never indicate corrosion if corrosion is not present. What is the probability of discovering corrosion?

There are three alternatives for producing a needed resource. The table below presents mean costs and variance of costs for each of them. If mean-variance dominance is applied to these alternatives then